= Self-dual circle current algebra
{title2=$SU(2)_L\times SU(2)_R$}
At $R=\sqrt{\alpha'}$, a chiral <compact boson> has <operator product expansion> $Y_L(z)Y_L(w)\sim-\alpha'\log(z-w)/2$. The currents $J^3=i\partial Y_L/\sqrt{\alpha'}$ and $J^\pm=:\!e^{\pm2iY_L/\sqrt{\alpha'}}\!:$ have <conformal weight> one. Contractions give $J^3(z)J^3(w)\sim1/[2(z-w)^2]$, $J^3(z)J^\pm(w)\sim\pm J^\pm(w)/(z-w)$ and $J^+(z)J^-(w)\sim1/(z-w)^2+2J^3(w)/(z-w)$. These are the level-one <SU(2) Lie algebra> currents. The right-moving copy supplies a second factor. Combining a current with a noncompact coordinate derivative gives a massless <string vertex operator> for each of the six vectors; four are additional to the generic two Cartan vectors.
Back to article page
